Question

Triangle XYZ is reflected over its hypotenuse to create a kite.

What is the approximate distance from Y to Y’? Round to the nearest tenth.

A. 4.6 units
B. 5.4 units
C. 8.0 units
D. 9.2 units (dumb answers will be reported)

Answer 1

The angle between line XZ and line XY is given by:

$x = atan (\frac{12}{5}) x = 67.38$

Then, the height from vertex Y to horizontal line XZ is:

$h = 5 sine (67.38) h = 4.62$

Then, the distance from Y to Y 'is given by:

$YY '= 2h YY '= 2 (4.62) YY '= 9.2$

Answer:

the approximate distance from Y to Y 'is:

D. 9.2 units

Answer 2

Trigonometric functions are the ratio of different sides of a right-angled triangle. The distance between the points Y and Y' is 9.2 units.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

XY = XY' = 5 units

YZ = Y'Z = 12 units

XZ = 13 units

In ΔXYZ,

We know that in a right-angled triangle, we can apply trigonometric function, therefore, for ∠YXZ

$\rm Tan(\theta) = \dfrac{Perpendicular}{Base}\\\\Tan(\angle YXZ) = \dfrac{YZ}{XY}\\\\Tan(\angle YXZ) = \dfrac{12}{5}\\\\Tan(\angle YXZ) = 2.4\\\\\angle YXZ = Tan^{-1}\ 2.4\\\\\angle YXZ = 67.38^o$

In ΔXYE,

$\rm Sin(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\Sin(\angle XYE) = \dfrac{YE}{XY}\\\\SIn(67.38^o) = \dfrac{YE}{5}\\\\YE = 4.6154$

Thus, the length of the line YE is 4.6154 units.

Now, we know that the ΔXY'Z is the reflection of the ΔXYZ, therefore, the length of the line YE=Y'E. The distance between the point Y and Y' can be written as,

YY' = YE+EY'

YY' = 4.6154 + 4.6154

YY' = 9.23

YY' = 9.2 units

Hence, the distance between the point Y and Y' is 9.2 units.

Learn more about Trigonometric functions:

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